Method and system for resonant operation of a reflective spatial light modulator

ABSTRACT

A method of activating a micro-mirror includes applying a first electrode voltage to one or more electrodes associated with the micro-mirror. The micro-mirror is positioned at a first positive deflection angle during a portion of the application of the first electrode voltage. The method also includes maintaining the first electrode voltage for a first predetermined time and applying a second electrode voltage to the one or more electrodes. The micro-mirror rotates to a first negative deflection angle during a portion of the application of the second electrode voltage. The method further includes maintaining the second electrode voltage for a second predetermined time and applying a third electrode voltage to the one or more electrodes. The micro-mirror is positioned at a second positive deflection angle greater than the first positive deflection angle during a portion of the application of the third electrode voltage.

CROSS-REFERENCES TO RELATED APPLICATIONS

The following two regular U.S. patent applications (including this one)are being filed concurrently, and the entire disclosure of the otherapplication is incorporated by reference into this application for allpurposes:

-   -   application Ser. No. 11/418,941, filed May 4, 2006, entitled        “Reflective Spatial Light Modulator With High Stiffness Torsion        Spring Hinge”; and    -   application Ser. No. 11/429,376, filed May 4, 2006, entitled        “Method and System for Resonant Operation of a Reflective        Spatial Light Modulator”.

BACKGROUND OF THE INVENTION

This present invention relates generally to spatial light modulators.More particularly, the invention relates to a method and structure forfabricating and/or operating a spatial light modulator with a highstiffness torsion spring hinge. Merely by way of example, the inventionhas been applied to initializing the micro-mirrors of a spatial lightmodulator using a resonant activation process. Additionally, theinvention has been applied to a method of operating a spatial lightmodulator in a display application using a dynamic switching mode. Themethod and structure can be applied to spatial light modulators as wellas other devices, for example, micro-electromechanical sensors,detectors, and displays.

Spatial light modulators (SLMs) have numerous applications in the areasof optical information processing, projection displays, video andgraphics monitors, televisions, and electrophotographic printing.Reflective SLMs are devices that modulate incident light in a spatialpattern to reflect an image corresponding to an electrical or opticalinput. The incident light may be modulated in phase, intensity,polarization, or deflection direction. A reflective SLM is typicallycomprised of an area or two-dimensional array of addressable pictureelements (pixels) capable of reflecting incident light.

Stiction is a common problem encountered in contacting MEMS devices suchas spatial light modulators. A micro-mirror light modulator is oneexample which in operation switches rapidly between two rotated position(on and off). The micro-mirror is typically supported by a torsionspring hinge and actuated by a bias voltage applied between the mirrorand one of two electrodes (for a binary mirror). The electrode driveforce is attractive and the micro-mirror is typically stopped by alanding pad or post. The force (torque) of the torsion spring willrestore the mirror to its equilibrium (un-rotated) position when thebias voltage is removed or reduced.

An adhesion force occurs when the micro-mirror contacts the landing pad,know as the stiction force. The origin of the stiction force typicallyarises from capillary force, electrostatic force due to contactpotential or dielectric, and Van Der Walls force. The relativecontribution of these three components depends on the geometry of thecontact as well as the materials of the contact and the environment thedevice is operating in. Thus stiction is a complex problem. When thestiction force equals and exceeds the restoring force of the torsionhinge, the micro-mirror will stick to the landing pad and causes failureof the device. When the stiction force varies in time (due to chargingfor example) it will affect the dynamic performance of the mirror, suchas its switching speed.

A number of solutions have been applied to reduce the stiction of a MEMSdevice. A typical example is to apply a molecular layer on theinterfaces to reduce the adhesion force between the contacting surfaces.Coating of some type of SAM molecules to convert the surface to behydrophobic is one method that effectively reduces the capillary forcebetween the contacting surfaces. In alternate methods of the prior art,a stiff landing spring is added as a landing pad, in addition to thetorsion hinge of the mirror. An overdrive pulse is applied to actuatethe landing spring (bending mode) which will then bounce themicro-mirror away from the contacting point (landing pad) and thetorsion spring will restore the mirror to its non-rotated position. Acombination of two or more anti-stiction solutions are often employed toimprove the device performance as well as its reliability.

In principle, so long as the restoring force and the torsion springforce (F_(hinge)) is greater than the stiction force (F_(stiction)) thenthe device should function properly. To increase the stiffness of thetorsion spring, one can increase its cross-section and reduce itslength. This approach is particularly applicable for a torsion springhinge made of materials with high Young's modulus and yield stress. Asingle crystalline silicon hinge is ideal for implementing this conceptas its Young's modulus is more than twice that of aluminum and its yieldstress, more than ten times that of aluminum.

Solving the stiction problem with high stiffness torsion spring mightappear to be the simplest solution. In general it also improvesperformance (by increasing the resonant frequency) and themanufacturability of the device. However, there are undesirableconsequences of a stiff hinge. First, it requires higher actuationvoltage to pull down or switch the micro-mirror. Second, the highactuation voltage will lead to more acceleration of the micro-mirrorduring switching and hence more impact of the micro-mirror on thelanding pad, which will accelerate the wear and increase the stiction.

Thus there is a need in the art for methods and systems to overcomethese drawbacks and to allow a practical implementation for using stifftorsion springs to overcome stiction forces and improve long termreliability in a MEMS device.

SUMMARY OF THE INVENTION

According to the present invention, techniques related to spatial lightmodulators are provided. More particularly, the invention relates to amethod and structure for fabricating and/or operating a spatial lightmodulator with a high stiffness torsion spring hinge. Merely by way ofexample, the invention has been applied to initializing themicro-mirrors of a spatial light modulator using a resonant activationprocess. Additionally, the invention has been applied to a method ofoperating a spatial light modulator in a display application using adynamic switching mode. The method and structure can be applied tospatial light modulators as well as other devices, for example,micro-electromechanical sensors, detectors, and displays.

According to an embodiment of the present invention, a method ofactivating a micro-mirror is provided. The method includes applying afirst electrode voltage to one or more electrodes associated with themicro-mirror. The micro-mirror is positioned at a first positivedeflection angle during a portion of the application of the firstelectrode voltage. The method also includes maintaining the firstelectrode voltage for a first predetermined time and applying a secondelectrode voltage to the one or more electrodes. The micro-mirrorrotates to a first negative deflection angle during a portion of theapplication of the second electrode voltage. The second electrodevoltage is maintained for a second predetermined time. The methodfurther includes applying a third electrode voltage to the one or moreelectrodes. The micro-mirror is positioned at a second positivedeflection angle greater than the first positive deflection angle duringa portion of the application of the third electrode voltage.

According to another embodiment of the present invention, a method ofoperating a micro-mirror for a spatial light modulator is provided. Themethod includes positioning the micro-mirror at a first positioncharacterized by a first deflection angle. The micro-mirror ismaintained at the first position through the application of a firstelectrode voltage. The method also includes rotating the micro-mirrorand positioning the micro-mirror at a second position characterized by asecond deflection angle. The micro-mirror is positioned at the secondposition through the application of a second electrode voltage less thana static snap-in voltage.

According to yet another embodiment of the present invention, a methodof operating a micro-mirror for a spatial light modulator is provided.The method includes positioning the micro-mirror at a first positioncharacterized by a first deflection angle. The method also includesrotating the micro-mirror to a second position characterized by a seconddeflection angle. The absolute value of the second deflection angle isgreater than zero and less than the absolute value of the firstdeflection angle. The method further includes applying an electrodevoltage to position the micro-mirror at a second position characterizedby a third deflection angle.

According to an alternative embodiment of the present invention, amethod of operating a micro-mirror of a spatial light modulator fordisplay applications is provided. The method includes resonantlyactivating the micro-mirror. Resonantly activating the micro-mirrorincludes applying a first electrode voltage to one or more electrodesassociated with the micro-mirror. The micro-mirror is positioned at afirst positive deflection angle during a portion of the application ofthe first electrode voltage. Resonantly activating the micro-mirror alsoincludes maintaining the first electrode voltage for a firstpredetermined time and applying a second electrode voltage to the one ormore electrodes. The micro-mirror rotates to a first negative deflectionangle during a portion of the application of the second electrodevoltage. Resonantly activating the micro-mirror further includesmaintaining the second electrode voltage for a second predetermined timeand applying a third electrode voltage to the one or more electrodes tosnap-in the micro-mirror to a first activated position characterized bya first activated angle.

The method according to the alternative embodiment of the presentinvention also includes dynamically switching the micro-mirror from thefirst activated position to a second activated position. Dynamicallyswitching the micro-mirror includes removing the third electrodevoltage, thereby freeing the micro-mirror to rotate the micro-mirror toa dynamic angle position. The absolute value of the dynamic angle isgreater than zero and less than the absolute value of the firstactivated angle. Dynamically switching the micro-mirror also includesapplying an electrode voltage to position the micro-mirror at the secondactivated position.

Numerous benefits are achieved using the present invention overconventional techniques. For example, in an embodiment according to thepresent invention, a high stiffness torsion spring hinge is utilized toreduce sagging of the mirror plate, preventing contact between themirror plate and the electrode structure. In some embodiments, themanufacturing process for a high stiffness torsion spring hinge issimplified in comparison with conventional techniques. Moreover, in aspecific embodiment, the impact energy produced when the mirror platemakes contact with a landing structure is reduced. In addition, theelectrode voltage utilized to switch the micro-mirror from one activatedposition to another activated position is decreased. Additionally,constraints on electrode voltage waveform characteristics, for example,rise times and fall times, are reduced by embodiments of the presentinvention. Depending upon the embodiment, one or more of these benefitsmay exist. These and other benefits have been described throughout thepresent specification and more particularly below.

Various additional objects, features and advantages of the presentinvention can be more fully appreciated with reference to the detaileddescription and accompanying drawings that follow.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified diagram illustrating the general architecture ofan SLM according to an embodiment of the present invention;

FIG. 2 is a simplified cutaway perspective view of an array of SLMsaccording to another embodiment of the present invention;

FIGS. 3A-3C are simplified cross-section views of a symmetric mechanicalsystem (micro-mirror) supported by a torsion spring hinge at centerpoint according to an embodiment of the present invention;

FIG. 3D shows data illustrating the rotation of a micro-mirror accordingto an embodiment of the present invention;

FIG. 3E illustrates dynamic and static response waveforms according toan embodiment of the present invention;

FIG. 3F is a simplified graph illustrating mirror deflection angle as afunction of applied electrode voltage according to an embodiment of thepresent invention;

FIG. 4A is a simplified timing diagram illustrating a resonantactivation procedure according to an embodiment of the presentinvention;

FIG. 4B is a simplified graph showing mirror deflection angle as afunction of time according to an embodiment of the present invention;

FIGS. 4C and 4D are simplified cross-sectional illustrations of amicro-mirror in unactivated and activated positions, respectively,according to an embodiment of the present invention;

FIG. 5A is a simplified timing diagram illustrating a mirror switchingoperation according to an embodiment of the present invention;

FIG. 5B is a simplified graph showing mirror deflection angle as afunction of time during the mirror switching operation;

FIGS. 5C-5F are simplified cross-sectional illustrations of amicro-mirror at various times during the mirror switching operations;

FIG. 6 is a simplified flowchart illustrating a method of activating amicro-mirror according to an embodiment of the present invention; and

FIG. 7 is a simplified flowchart illustrating a method of operating amicro-mirror according to an embodiment of the present invention.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

According to the present invention, techniques related to spatial lightmodulators are provided. More particularly, the invention relates to amethod and structure for fabricating and/or operating a spatial lightmodulator with a high stiffness torsion spring hinge. Merely by way ofexample, the invention has been applied to initializing themicro-mirrors of a spatial light modulator using a resonant activationprocess. Additionally, the invention has been applied to a method ofoperating a spatial light modulator in a display application using adynamic switching mode. The method and structure can be applied tospatial light modulators as well as other devices, for example,micro-electromechanical sensors, detectors, and displays.

FIG. 1 is a simplified diagram illustrating the general architecture ofan SLM 100 according to an embodiment of the present invention. Theillustrated embodiment has three layers. The first layer is a mirrorarray 103 that has a plurality of deflectable micro-mirrors 202. In apreferred embodiment, the micro-mirror array 103 is fabricated from afirst substrate 105 that is a single material, such as single crystalsilicon. The micro-mirrors 202 are characterized by a perimeter of lessthan 80 μm, and alternately by a perimeter of less than 50 μm.Additional details related to SLMs using such an architecture aredescribed in U.S. patent application Ser. No. 10/756,936, entitledReflective Spatial Light Modulator, filed Jan. 13, 2004, commonlyassigned, and hereby incorporated by reference for all purposes.

The second layer is an electrode array 104 with a plurality ofelectrodes 126 for controlling the micro-mirrors 202. Each electrode 126is associated with a micro-mirror 202 and controls the deflection ofthat micro-mirror 202. Addressing circuitry allows selection of a singleelectrode 126 for control of the particular micro-mirror 202 associatedwith that electrode 126.

The third layer is a layer of control circuitry 106. This controlcircuitry 106 has addressing circuitry, which allows the controlcircuitry 106 to control a voltage applied to selected electrodes 126.This allows the control circuitry 106 to control the deflections of themirrors 202 in the mirror array 103 via the electrodes 126. Typically,the control circuitry 106 also includes a display control 108, linememory buffers 110, a pulse width modulation array 112, and inputs forvideo signals 120 and graphics signals 122. A microcontroller 114,optics control circuitry 116, and a flash memory 118 may be externalcomponents connected to the control circuitry 106, or may be included inthe control circuitry 106 in some embodiments. In various embodiments,some of the above listed parts of the control circuitry 106 may beabsent, may be on a separate substrate and connected to the controlcircuitry 106, or other additional components may be present as part ofthe control circuitry 106 or connected to the control circuitry 106.

In an embodiment according to the present invention, both the secondlayer 104 and the third layer 106 are fabricated using semiconductorfabrication technology on a single second substrate 107. That is, thesecond layer 104 is not necessarily separate and above the third layer106. Rather, the term “layer” is an aid for conceptualizing differentparts of the spatial light modulator 100. For example, in oneembodiment, both the second layer 104 of electrodes is fabricated on topof the third layer of control circuitry 106, both fabricated on a singlesecond substrate 107. That is, the electrodes 126, as well as thedisplay control 108, line memory buffers 110, and the pulse widthmodulation array 112 are all fabricated on a single substrate in oneembodiment. Integration of several functional components of the controlcircuitry 106 on the same substrate provides an advantage of improveddata transfer rate over conventional spatial light modulators, whichhave the display control 108, line memory buffers 110, and the pulsewidth modulation array 112 fabricated on a separate substrate. Further,fabricating the second layer of the electrode array 104 and the thirdlayer of the control circuitry 106 on a single substrate 107 providesthe advantage of simple and cheap fabrication, and a compact finalproduct. After the layers 103, 104, and 106 are fabricated, they arebonded together to form the SLM 100. Additional examples of methods forjoining the substrates to form a bonded substrate structure aredescribed in U.S. patent application Ser. No. 10/756,923, entitledFabrication of a Reflective Spatial Light Modulator, filed Jan. 13,2004, commonly assigned, and hereby incorporated by reference for allpurposes.

As illustrated in FIG. 1, the substrate 105 includes a number ofstandoff regions extending from a lower portion of the substrate andarranged in an array as a waffle pack grid pattern. The standoff regionsare adapted to align with bonding areas located between adjacentelectrodes 126. Mirrors 202 are formed in the upper layers of substrate105 by a release process in later stages of processing. In some designs,the standoff regions provide mechanical support for the mirror structureand are not moveable. Thus, light reflected from the upper surfaces ofthe standoff structures reduces the contrast of the optical systemincorporating the spatial light modulator. In some designs, an absorbentmaterial may be applied to the upper surfaces of the standoff regions toreduce reflections. However, these approaches reduce the fill factor ofthe array, potentially degrading system performance.

FIG. 2 is a simplified cutaway perspective view of an array of SLMsaccording to another embodiment of the present invention. Asillustrated, this cutaway view is merely representative of the array ofSLMs at various stages of processing. As described more fully below,independent control of the SLMs in an array is utilized in embodimentsaccording to the present invention to form images in displayapplications and other apparatus.

As illustrated in FIG. 2, the array of SLMs is mounted on a supportsubstrate 210. In some embodiments, the support substrate is a siliconsubstrate with CMOS control circuitry fabricated using semiconductorprocessing techniques. Multi-level electrodes 212 are coupled to thesupport substrate 210. As illustrated in FIG. 2, the multi-levelelectrodes comprise two complementary electrodes 214 (referred to aselectrode E) and 216 (referred to as electrode Ē) positioned on oppositesides of an integrated standoff structure 220. As described more fullybelow, in an embodiment, drive voltages of opposite polarity areprovided to the complementary electrodes, providing electrostaticattraction forces acting on the micro-mirror plates 230. In otherembodiments, the drive voltages are characterized by differing voltages,although not necessarily of opposite polarity. Moreover, in somealternative embodiments, the repulsion forces generated by theelectrodes is negligible, with the restoring torque stored in thetorsion spring hinge providing a torque sufficient to return the mirrorto an unactivated position.

In operation, the individual reflective elements or pixels making up anarray of micro-mirrors in an SLM are selectively deflected, therebyserving to spatially modulate light that is incident on and reflected bythe micro-mirrors in the SLM. In order to deflect the micro-mirrors, avoltage is applied to the complementary electrodes 214 and 216 and themirror plate to cause the mirror to rotate about the torsion springhinge 232. As will be evident to one of skill in the art, the pixels areadapted to rotate in both clockwise and counter-clockwise directionsdepending on the particular electrode voltages. When the voltages areremoved, the torque present in hinge 232 causes the mirror plate 230 toreturn to the unactivated position illustrated in FIG. 2.

FIG. 2 illustrates an embodiment of the present invention in which thecomplementary electrodes 214 and 216 are multi-level electrodes withraised central portions adjacent the center of the micro-mirror plates.Such multi-level electrodes reduce the distance between the top of theelectrode surface and the micro-mirror plates, thereby decreasing themagnitude of the addressing voltages used to actuate the micro-mirrorplates. However, embodiments of the present invention are not limited tomulti-level electrodes. In alternative embodiments, other electrodegeometries are utilized. One of ordinary skill in the art wouldrecognize many variations, modifications, and alternatives.

As illustrated in FIG. 2, each micro-mirror plate 230 is coupled to thesupport substrate 210 by integrated standoff structure 220 and a torsionspring hinge 232. Referring to one of the micro-mirrors 240, uponactuation of the electrodes, the micro-mirror plate rotates in a planeorthogonal to the longitudinal axis of the torsion spring hinge. In someembodiments, the longitudinal axis of the torsion spring hinge isparallel to a diagonal of the micro-mirror plate. The motion of themicro-mirror is arrested by landing structures 222. In order to providetwo actuated positions, complementary sets of landing structures 222 aand 222 b are provided on opposite sides of the integrated standoffstructure. Thus, landing structures 222 a arrest the motion of themicro-mirrors at a first actuated position and landing structures 222 barrest the motion of the micro-mirrors at a second actuated position.According to embodiments of the present invention, the micro-mirrors aretilted at predetermined angles in the actuated states, providing forcontrolled reflection of incident radiation. Embodiments of the presentinvention are not limited to the particular architecture describedabove. In alternative embodiments, a single landing pad located at thelanding position of the mirror tip is used in place of the two landingposts. Moreover, two posts positioned at outer edges of the hinge may beused to replace the single standoff structure illustrated. One ofordinary skill in the art would recognize many variations,modifications, and alternatives.

The support substrate 210, the integrated standoff structures 220, andthe micro-mirror plates 230 are joined using a substrate bonding processaccording to some embodiments of the present invention. In otherembodiments, these structures are fabricated using a combination ofdeposition, patterning, etching, wafer bonding, and other semiconductorprocessing techniques. As illustrated in FIG. 2, reflective surfaces 240are formed on the micro-mirror plates, providing an array of SLMs withhidden hinges. For purposes of clarity, the spacing between adjacentmicro-mirrors is illustrated in FIG. 2 as a significant fraction of themirror dimensions. As will be evident to one of skill in the art,reductions in the space between mirrors will result in an increased fillratio and improved image quality in display applications. The spacingbetween adjacent micro-mirrors is generally defined usingphotolithographic processes, providing high fill ratio designs.Additional details related to the fabrication of integrated standoffstructures and multi-level electrodes are described in U.S. patentapplication Ser. No. 11/250,320, entitled Spatial Light Modulator WithMulti-Layer Landing Structures, filed Oct. 13, 2005, commonly assigned,and hereby incorporated by reference for all purposes.

During conventional operation of the SLM, the mirror is typicallyswitched between a center or unactivated position and two complementaryactivated positions with equal and opposite deflection angles. In eitherof the activated positions, stiction forces present between the mirrorplate of the micro-mirror and the landing structure, for example, thelanding posts 222 illustrated in FIG. 2, may prevent the micro-mirrorfrom returning to the center position. As will be evident to one ofskill in the art, pixels of a display sticking in such an activatedstate is undesirable. Accordingly, embodiments of the present inventionprovide torsion spring hinges with increased stiffness to overcomestiction forces and free the micro-mirror from sticking in an activatedstate. As described below, high stiffness springs also provide forincreased operational speed and manufacturability, among other benefits.A single crystalline silicon hinge is ideal for implementing thisconcept as its Young's modulus is more than twice that of aluminum andits yield stress, more than ten times that of aluminum. It in generalalso improves performance (by increasing the resonant frequency) and themanufacturability of the device.

Consider a symmetric mechanical system (micro-mirror) supported by atorsion spring hinge at center point as depicted in FIGS. 3A-3C. Underthe condition of no dissipation, this is a conservative mechanicalsystem, i.e. its kinetic energy can be converted into potential energyand vice versa. If the mirror (flat state being the equilibriumposition) is initialized to the counter clockwise rotation with angle α(on-sate, FIG. 3A) and released, it will rotate clockwise to an angle of−α (off-state, FIG. 3B). In such an ideal system, the mirror can rotatefrom the on-state to the off-state without any additional energy.Furthermore, when the mirror reaches the off-state, its speed is zeroand thus generates no impact at the contact.

In a real system, dissipation is inevitable due to external interactionwith air or internal heat (phonon) generation. In such a case, themirror should rotate to −α′ (|−α′|<|−α|), which should be very close theoff-state if the dissipation is small. This is indeed observed with areal device. FIG. 3D shows data illustrating the rotation of amicro-mirror according to an embodiment of the present invention. Asshown in FIG. 3D, only a small amount energy (ΔE) is required to switchthe mirror to the full off-state, (−12 degrees) if it is supplied whenthe mirror reaches −α′. Properly matching the input energy to the amountdissipated can also minimize the landing impact and wear of the contact.

Implementation of the above concept can be realized with a dynamic drivewaveform as illustrated in FIG. 3E (solid curve in lower left panel).Consider the mirror is initialized to the off-state, holding by avoltage at the middle level. This voltage then drops and held at therelease-level for an interval t₁, allowing the mirror to swing to theopposite side. When it reaches the maximum rotation angle −α′, thevoltage level is promptly raised to the capture-level for an interval oft₂, to pull the mirror to the on-state before it resets to thehold-level. A similar wave form can be used to switch the mirror fromthe on-state to off-state.

Based on the nonlinear characteristics of the static response showing inFIG. 3E (lower right), if the mirror can swing to the opposite sideclose to the maximum angle, then a lower pull-down voltage (than thestatic pull-down voltage) will suffice to pull the mirror down to the“snap-in” position. This is another significant benefit of using thedynamic drive waveform.

The aforementioned dynamic switching concept can be applied to an arrayof identical micro-mirror device. The mechanical property of theindividual hinge needs not be identical, though the margin of operationwill depend on the uniformity of the array (see static response curve inFIG. 3E). Furthermore by addressing the electrodes of the mirror tocreate a differential bias voltage between the two sides of a mirror,one selectively switches the ones as desired, leaving the other to stayon the same side (see the dashed curve in FIG. 3E, left panels).

The dynamic switching scheme discussed above required the mirror beinitialed to one of its full rotated state. With a high stiffnesstorsion hinge, it requires a higher DC pull-down voltage and hence adevice having higher dielectric strength to avoid electrical breakdown.

Another embodiment of the present invention combines resonant excitationwith the dynamic switching to initialize the mirror to one of the fullrotated states at a lower actuation voltage compared to its DC pull downvoltage. This embodiment will be discussed in additional detail withrespect to FIGS. 4A and 4B.

Since the micro-mirror is an oscillator with a reasonable quality factor(Q), one can drive the device to resonance with an AC waveform(sinusoidal, for example) of a modest amplitude. As the angle of mirrorswing increases to near “snap-in” position, say α′, the switching pulseis applied synchronously to capture the mirror to the “snap-in”position. The mirror is initialized and the excitation waveform can beremoved.

FIG. 3F is a simplified graph illustrating mirror deflection angle as afunction of applied electrode voltage according to an embodiment of thepresent invention. As illustrated in FIG. 3F, at a zero applied voltage,the mirror deflection or tilt angle (θ) is zero, a condition associatedwith the micro-mirror prior to power-up. As the voltage applied to theelectrodes and mirror plate increases, the mirror begins to rotate underthe influence of the applied voltage in a first direction as illustratedby curve 310. As shown in FIG. 3F, the mirror rotates in a directioncharacterized by a positive tilt angle, although a negative tilt angleis also utilized in other embodiments.

When the mirror plate deflects past the “snap-in” or “pull-in” voltage,V_(S), (approximately 150 V in an embodiment), the restoring mechanicalforce or torque of the hinge can no longer balance the electrostaticforce or torque and the mirror plate “snaps” down toward the electrodeto achieve full deflection (θ_(max)), limited only by motion stopsprovided by the SLM structure. This full deflection position issometimes referred to as an activated position. Due to stiction forcesand other effects, micro-mirrors provided according to embodiments ofthe present invention display hysteresis as illustrated in FIG. 3F. Inother words, the voltage V_(R) required to hold the mirror plates in thedeflected position is less than that required for the actual deflection.Accordingly, in the activated positions, application of voltages lessthan V_(S) and greater than V_(R) result in a condition in which theelectrostatic force due to the applied voltage and stiction are greaterthan the restoring force due to the torque stored in the spring. At thevoltage V_(R), the electrostatic attraction and stiction forces arebalanced by the restoring force in the spring.

To release the mirror plate from its fully deflected position, thevoltage is lowered to a value below the snap-in voltage V_(S), to areleasing voltage V_(R), as illustrated in FIG. 3F. Below the releasevoltage, the mirror rotates as illustrated by line 312, returning to theoriginal undeflected position as the voltage is reduced to zero. Thenon-linearity in curve 310 results from the capacitance between themirror plates and the support substrate being a function of deflectionangle. As the mirror approaches the activated position, the increase incapacitance results in an increase in the electrostatic attraction forcefor a given voltage change.

Increases in hinge stiffness generally result in an increase inrotational velocity of the mirror plate, providing the benefit ofincreased operational speed. As will be evident to one of skill in theart, the angular frequency of a torsion spring hinge is proportional tothe square root of the spring constant divided by the mass: ω=√{squareroot over (K/m)}. Thus, embodiments of the present invention utilizetorsion spring hinges with increased spring constants compared toconventional hinges, increasing the angular velocity of the mirror platecoupled to the hinge. Additionally, an increase in spring constantresults in an increased ability to overcome stiction forces presentbetween the mirror plate and the landing structure. Reliability andlifetime are enhanced by embodiments of the present invention in whichstiction forces are overcome by the torque stored in the torsion springhinge with reduced or without reliance on lubricants. Furthermore,embodiments of the present invention provide spatial light modulatorsystems with increased manufacturability over conventional systems sincethe length of the spring can be decreased as the stiffness is increased.

However, although increasing the stiffness of the flexible member ortorsion spring hinge generally results in an increase in both theelectrode voltages shown as V_(S) and V_(R) in FIG. 3F. Moreover, as therotational velocity of the mirror plate increases with the springstiffness, an increase in the impact energy may be experienced when themirror plate makes contact with motion stops, adversely impactingreliability. Embodiments of the present invention provide solutions tothese issues through the use of resonant activation and dynamicswitching as described more fully below.

Referring to FIG. 3F, as the voltage approaches V_(S) along curve 310,the slope of the mirror deflection angle versus voltage increasesdramatically. The rapid change in angle as the mirror “snaps” to thefull deflection angle results in the mirror plate striking the motionstops with an undesirable impact energy. Thus, as described more fullybelow, to overcome this undesired result, embodiments of the presentinvention provide a resonant activation process that reduces the impactenergy, thereby providing increased device lifetime and reliabilityamong other benefits.

FIG. 4A is a simplified timing diagram illustrating a resonantactivation procedure according to an embodiment of the presentinvention. The voltage applied to the first complementary electrode(V_(L)) is shown as a constant value as a function of time. The voltageapplied to the second complementary electrode (V_(R)) is zero in FIG. 4Aand thus not illustrated.

The voltage applied to the mirror (bias voltage) is represented by thedotted line V_(M) and varies as a function of time. At an initial timet₀, the mirror voltage is equal to zero and the mirror is in anunactivated position. FIG. 4C is a simplified cross-sectionalillustration of a micro-mirror in the unactivated position at time t₀.As illustrated in FIG. 4C, the mirror deflection angle is equal to zero.In FIG. 4C, the voltage applied to the various components of the SLM arerepresented by the voltage symbols V_(L), V_(R), and V_(M). Merely byway of example, in a video display application, time to would representa time when the video display system is turned off prior to power-up.

At a time t₁, the voltage applied to the mirror is changed to V₁. Asdescribed more fully below, the voltage V₁ is less than the staticsnap-in voltage V_(S) illustrated in FIG. 3F. As an example, the mirrorvoltage V₁ is about −100 V in an embodiment. In other embodiments, themirror voltage ranges from about −35 V to about −170 V. The voltage willdepend on the particular applications. The mirror voltage V_(M) ismaintained at V₁ for a predetermined time Δt between t₁ and t₂. Thepredetermined time Δt is selected based on a number of parametersincluding, for example, the torsion spring stiffness and the mirrordimensions. Although the time Δt illustrated in FIG. 4A is equal foreach of the three voltage pulses between t₁ and t₂, t₅ and t₆, and t₇and t₈, respectively, this is not required by the present invention.

The length of each pulse may be varied in other embodiments asappropriate to the particular implementation. Moreover, the amplitude ofthe three voltage pulses shown in FIG. 4A may be varied from pulse topulse or during each pulse depending on the application. Furthermore, aswill be evident to one of skill in the art, the number of pulsesutilized may be varied to increase or decrease the number of pulses as afunction of, for example, the voltage amplitude and the system Q factor.

FIG. 4B is a simplified graph showing mirror deflection angle as afunction of time according to an embodiment of the present invention.When the mirror voltage is set to V₁ at time t₁, the mirror begins todeflect at a negative angle as illustrated in FIG. 4B. The deflectionangle of the mirror increases in a first (negative) rotation directionand reaches a local maximum at time t₂, coincident with the end of thefirst voltage pulse. At time t₂, the mirror voltage is reduced to zeroand the mirror begins to counter-rotate in response to the torque on thetorsion spring hinge. At time t₃, the mirror is counter-rotating towardsa local maximum between time t₃ and t₄. At time t₄ the mirror isrotating in the first direction back toward the center positionillustrated in FIG. 4C. Thus, a series of mirror oscillations isinitiated by applying the voltage pulse during time t₁ and t₂ to themirror. Utilizing the high stiffness hinge described herein, the initialoscillation amplitude is small, increasing as voltage pulses arerepeatedly applied to the mirror plate.

At time t₅, the mirror voltage is set to V₁ and the deflection angle ofthe mirror increases once again in the first rotation direction. As willbe evident to one of skill in the art, the timing of the second pulsebeginning at time t₅ is selected to resonantly enhance the rotation andcounter-rotation of the mirror. As an example, for a representative highstiffness hinge, the resonant frequency is about 1.5 MHz. Of course, theparticular resonant frequency will be a function of the materials anddimensions of the SLM structure, such as the hinge and mirror plate.Accordingly, the amplitude of the deflection angle oscillationsincreases as a function of time as illustrated in FIG. 4B. At time t₆,the mirror once again reaches a local maximum in the first rotationdirection. When the mirror voltage is once again reduced to zero at timet₆, the mirror begins counter-rotating, reaching a local maximum betweentime t₆ and t₇ at a greater angle than achieved for the local maximumbetween time t₃ and t₄.

The third mirror voltage pulse is applied at time t₇ and extends untiltime t₈. At time t₉, which corresponds to the mirror being in theposition illustrated in FIG. 4C, but rotating in the first direction,the mirror voltage is once again set at V₁ and the mirror continuesrotating in the first rotation direction under the influence of theapplied voltage. At time t₁₀, the mirror reaches an angle defined as thedynamic angle. The dynamic angle is the angle at which the mirrorreaches what would be a local maximum. As illustrated in FIG. 4B, aftertime t₁₀, the mirror snaps in to the snap-in angle (−θ_(max)), which isa maximum deflection angle. It should be noted that through the use ofthe resonant activation mode described herein, the voltage V₁ utilizedto achieve the fully activated mirror position illustrated in FIG. 4D attime t₁₁ is less than a static snap-in voltage.

Referring to FIGS. 4A and 4B, at time t₉-t₁₀, the distance between themirror plate and the electrodes is less than the distance at time t₀.Thus, the voltage needed to rotate the mirror to the snap-in angle(−θ_(max)) is reduced from the static snap-in voltage, in which themirror is rotated from the position illustrated in FIG. 4C to theposition illustrated in FIG. 4D by the application of a single voltagehigher than voltage V₁.

In applications using SLMs, digital operation is achieved by reflectinglight off pixels positioned in one of two activated positions, θ_(max)and −θ_(max), respectively. During an initial start-up phase, all pixelsin a given SLM are resonantly activated using the resonant turn-onsequence illustrated in FIGS. 4A and 4B. As a result, the pixels are allpositioned to either reflect light toward a viewing screen or an opticaldump, depending on the particular implementation. In an alternativeembodiment, the position of the initial start-up phase varies, withmirrors positioned as either θ_(max) or −θ_(max) in an ordered orrandomized manner. The initial position is somewhat arbitrary, since, asthe display of video signals begins, the positions of the pixels aremodulated in response to the signal using a pulsed waveform as describedbelow. One of ordinary skill in the art would recognize many variations,modifications, and alternatives.

According to embodiments of the present invention, the micro-mirrors inan array are electromechanically bistable devices. Given a specificvoltage between the releasing voltage and the snapping voltage, thereare two possible deflection angles at which the mirror plate may be,depending on the history of mirror plate deflection. Therefore, themirror plate deflection acts as a latch. We believe these bistabilityand latching properties exist since the mechanical force required fordeflection of the mirror plate is roughly linear with respect todeflection angle, whereas the opposing electrostatic force is inverselyproportional to the distance between the mirror plate and the electrode.

In some conventional SLM systems, the SLM operation of a pixel involvesrotating the micro-mirror from a center position to a first activatedposition, returning the mirror to the center (unactivated) position, andthen rotating the micro-mirror to a second activated position. As anexample, the two activated positions may be tilted at equal and oppositerotation angles. Embodiments of the present invention utilize thepotential energy stored in the hinge when at a first activated positionto reduce the snap-in voltages used to position the mirror in a secondactivated position. This method of operating an SLM is referred to asdynamic switching and reduces the electrode voltages utilized duringmirror operation.

FIG. 5A is a simplified timing diagram illustrating a mirror switchingoperation according to an embodiment of the present invention. Thevoltages applied to the complementary electrodes (V_(L) and V_(R)) areswitched at a time to as illustrated in FIG. 5A. The mirror voltage ischanged from a first voltage V₁ to a second voltage V₂ at time t₁. In anembodiment, the voltage V₁ is −120 V and the voltage V₂ is −90 V. Inother embodiments, the values of the voltages V₁ and V₂ range from about−35 V to about −170 V and from about −30 V to about −160 V,respectively. Of course, the values utilized will depend on theparticular applications. As illustrated in FIG. 5C, the mirror ispositioned at a first maximum rotation angle at time t₀.

FIG. 5B is a simplified graph showing mirror deflection angle as afunction of time during the mirror switching operation. In response tothe change in the mirror voltage at time t₁, the mirror is released andbegins rotating in the clockwise direction due to the torque stored inthe torsion spring hinge. Because of the high stiffness hinge providedby embodiments of the present invention, stiction forces present in thevicinity of the left electrode are less than the torque stored in thetorsion spring hinge. Moreover, the high stiffness hinge results in arapid rotation of the mirror in the clockwise direction. In someembodiments of the present invention, the transition time from theposition illustrated in FIG. 5C to the position illustrated in FIG. 5Fis about 0.3 μs to about 2.0 μs.

As will be evident to one of skill in the art, the high stiffness hingeenables the micro-mirror to rotate away from the activated positionshown in FIG. 5C at a high angular rate under the influence of thespring alone, independent of electrode voltages applied to thecomplementary electrodes or the mirror plate. In designs utilizingconventional weak hinges, the rotation rate of the mirror plate isgoverned by the various applied voltages, not the response inherent inthe high stiffness hinges described herein. In a specific embodiment,the maximum rotation rate of the mirror plate is in a predeterminedrange, for example from about 20 degrees per microsecond to about 115degrees per microsecond. Preferably the rotation rate ranges from about45 degrees per microsecond to about 70 degrees per microsecond. One ofordinary skill in the art would recognize many variations,modifications, and alternatives.

At time t₂, the mirror passes through an undeflected or center positionas it continues to rotate in the clockwise direction. The mirror reacheswhat would be a local maximum at time t₃. The pulse width δt is selectedso that as the mirror rotation angle approaches the dynamic snap-inangle (θ_(dynamic)) at time t₃, the mirror voltage is changed back tothe voltage V₁. Among other factors, the close proximity of the mirrorplate to the right electrode enables the mirror to be snapped-in at avoltage less than the static snap-in voltage, positioning the mirror ata second maximum rotation angle (θ_(max)) at time t₄. Thus, in anembodiment, the torque stored in the spring is used to rotate themirror, independent of applied voltages, to a rotation angle nearlyequal to the maximum rotation angle. As a result of the use of thedynamic switching operation, the voltage needed to actuate the mirrorare reduced. A similar dynamic switching operation is utilized to returnthe mirror to the first maximum rotation angle.

According to embodiments of the present invention, the pulse width δt,the characteristics of the flexible member or hinge coupled to themicro-mirror, particularly the stiffness of the hinge, and the maximumrotation angle of the micro-mirror are related to facilitate a dynamicswitching operation. After initialization in one of the two activatedpositions (θ_(max) and −θ_(max)), the duration δt of the mirror voltagepulse is selected to end the voltage pulse coincident with the mirror'srotation angle reaching the dynamic snap-in angle. In a specificembodiment, the high stiffness torsion spring hinge reduces the time δtto a value less than that characteristic of conventional hinges used formicro-mirrors in display applications. Merely by way of example, thetime δt is approximately equal to 1.0 μs in an embodiment. In otherembodiments, the value of δt ranges from about 0.3 μs to about 2.0 μs.Of course, the particular value will depend on the various applications.

Referring once again to FIG. 5B, damping in the torsion spring hingeresults in the mirror rotating to the dynamic rotation angle, which isless than the maximum angle. In other words, in the absence of dampingor losses in the hinge, the mirror, when released at one maximumrotation angle would rotate to the complementary maximum rotation angle.The angular velocity of the mirror rotation starts at zero at time t₁,reaches a peak at time t₂, and returns to zero at time t₃. Because theangular velocity at time t₃ is zero, the impact energy when the mirrorsnaps-in shortly after time t₃ is reduced compared to conventionaldesigns.

The duration of the mirror voltage pulse δt influences the impact energywith which the mirror strikes the electrodes, landing structures, orother motion stops. The impact energy is the kinetic energy of themirror at contact with motion stops after rotation from a firstactivated position to a second activated position. Preferably, theenergy stored in the high stiffness hinge when the mirror is in anactivated position provides the majority of energy needed to rotate themirror from the first activated position to the second activatedposition.

The mirror voltage pulse is timed to return to voltage V₁ when themirror is at the dynamic snap-in angle, minimizing the distance betweenthe mirror plate and electrode, and thereby reducing the applied voltageused to position the mirror at the second activated position. Moreover,with the distance between the mirror plate and the electrode reduced,the distance over which the mirror is accelerated as it rotates from thedynamic snap-in angle to the maximum deflection angle is reduced,thereby limiting the angular velocity of the mirror at impact. Incontrast with conventional designs using static snap-in voltages,embodiments of the present invention provide reductions in the impactenergy that contribute to enhanced lifetime and reliability. Thus,embodiments of the present invention provide not only reduced operatingvoltages and higher speed operation, but reduced mechanical impact.

The impact energy with which a micro-mirror contacts a landing structureis influenced by the magnitude of the electrode voltage utilized toachieve a snap-in condition. Most of the electrostatic energy impartedto the moving micro-mirror is absorbed on landing, causing stiction andwear. According to embodiments of the present invention, by reducing theelectrostatic energy required to snap-in the micro-mirror, improvedlifetime and wear resistance is achieved.

The electrostatic energy (E_(e)) required to snap-in a micro-mirror iscalculated using:

${E_{e} = {\frac{1}{2}{C(\alpha)}V^{2}}},$where C is the capacitance and V is the driving voltage.

Embodiments of the present invention using dynamic switching provide forsofter landings (reduced impact energy) by utilizing a lower drivingvoltage as compared to alternate systems. The lower driving voltage isV′=V−δV. Therefore the change in electrostatic energy is:δE _(e) =C(α)V·δVand

$\frac{\delta\; E}{E} = {\frac{{2 \cdot \delta}\; V}{V}.}$

Conservatively speaking, embodiments of the present invention providefor at least a 10% reduction in the driving voltage when using dynamicswitching. This results in a 20% reduction in impact energy. Formicro-mirrors with excellent structural uniformity, a minimum 20%reduction in driving voltage is possible, resulting in at least a 40%reduction in impact energy.

FIG. 6 is a simplified flowchart illustrating a method of activating amicro-mirror according to an embodiment of the present invention. Amethod 600 of resonantly activating one or more micro-mirrors in aspatial light modulator array is provided as follows. A first electrodevoltage is applied (610) to electrodes associated with the one or moremicro-mirrors. The application of the first electrode voltage results inthe micro-mirror being positioned at a first negative deflection angleduring a first time. Referring to FIG. 4B, at time t₂, the mirror platereaches a local maximum deflection angle. Although the angle illustratedat time t₂ is a negative deflection angle, one of ordinary skill in theart will appreciate that the initial rotation angle will depend on theparticular applications. In some embodiments, the initial rotation anglewill be a positive deflection angle.

The first electrode voltage applied to the electrodes is maintained(612) at the first electrode voltage for a first predetermined time. Inthe embodiment illustrated in FIG. 4A, the first predetermined time isΔt. Of course, the predetermined first time will depend on thecharacteristics of the torsion spring hinge, the magnitude of the firstelectrode voltage, and other factors. As illustrated in FIGS. 4A and 4B,the first predetermined time is selected so that the end of the firstvoltage pulse is aligned with the mirror plate reaching the localmaximum deflection angle.

A second electrode voltage is applied to the one or more electrodes(614). The application of the second electrode voltage results in themicro-mirror rotating to a first positive deflection angle during aportion of the application of the second electrode voltage. In aparticular embodiment, the second electrode voltage is ground.Responding to the torque stored in the torsion spring hinge, themicro-mirror rotates past zero and toward a positive deflection angle.As illustrated in FIGS. 4A and 4B, the micro-mirror is positioned at alocal maximum deflection angle at time between times t₃ and t₄. Thesecond electrode voltage is maintained for a second predetermined time(616). As will be evident to one of skill in the art, the secondpredetermined time is selected based on similar factors as discussed inrelation to the first predetermined time.

A third electrode voltage is applied to the one or more electrodes(618). The micro-mirror is positioned at a second negative deflectionangle as a result of the application of the third electric voltage. Thesecond negative deflection angle is greater than the first negativedeflection angle during a portion of the application of the thirdelectrode voltage. Referring once again to FIGS. 4A and 4B, in anembodiment, the third electrode voltage is applied during times t₅ andt₆ and is equal in amplitude to the first electric voltage. The thirdelectrode voltage is maintained for a third predetermined time (620).The second negative deflection angle is a local maximum at time t₆,which corresponds to the end of the third electric voltage pulse.

A fourth electrode voltage is applied to the one or more electrodes(622). The micro-mirror rotates to a second positive deflection anglegreater than the first positive deflection angle during a portion of theapplication of the fourth electrode voltage. The fourth electrodevoltage is maintained for a fourth predetermined time (624). A fifthelectrode voltage is applied to the one or more electrodes (626). Themicro-mirror is positioned at a third negative deflection angle greaterthan the second negative deflection angle during a portion of theapplication of the fifth electrode voltage. Referring to FIGS. 4A and4B, the fifth electrode voltage may be the voltage applied after timet₉. Of course, the total number of voltage pulses will depend on avariety of factors, including the torsion spring stiffness, themagnitude of the applied voltages, the system mass, and the like.According to embodiments of the present invention, resonant activationas illustrated in FIG. 6 is utilized to position the micro-mirror in afirst activated position illustrated time t₁₁.

The above sequence of steps provides a method for resonantly activatinga micro-mirror according to an embodiment of the present invention. Asshown, the method uses a combination of steps including a way ofapplying and maintaining a series of electrode voltages to resonantlyrotate the micro-mirror from an unactivated position to an activatedposition according to an embodiment of the present invention. Otheralternatives can also be provided where steps are added, one or moresteps are removed, or one or more steps are provided in a differentsequence without departing from the scope of the claims herein.

In the embodiment of the present invention illustrated in FIGS. 4A and4B, the amplitude, shape, and duration of the first and third voltagepulses are equal. However, this is not required by the presentinvention. In other embodiments, these characteristics are varied asappropriate to the particular application. For example, the shape of thevoltage pulse may not be square, but may be sinusoidal, triangular, andthe like. One of ordinary skill in the art would recognize manyvariations, modifications, and alternatives. Moreover, the length andtemporal positioning of the pulses may be varied as appropriate to theparticular application.

FIG. 7 is a simplified flowchart illustrating a method of operating amicro-mirror according to an embodiment of the present invention. Themethod 700 provides for dynamic switching of a micro-mirror from a firstactivated position to a second activated position. As an example, themicro-mirror may be positioned in the first activated position using amethod as described in relation to FIG. 6.

The micro-mirror is positioned at a first position characterized by afirst deflection angle (710). The micro-mirror is maintained at thefirst position through the application of a first electrode voltage(712). In the embodiment illustrated in FIGS. 5A and 5B, the firstdeflection angle is a snap in angle with a negative magnitude. Themicro-mirror is rotated (714). In an embodiment, the rotation of themirror is accomplished by releasing the first electrode voltage,resulting in rotation of the mirror under the influence of the storedtorque in the torsion spring hinge. The micro-mirror is positioned at asecond position characterized by a second deflection angle (716). Themicro-mirror is positioned at the second position through theapplication of a second electrode voltage less than a static snap-involtage.

The above sequence of steps provides a method for dynamically switchinga micro-mirror according to an embodiment of the present invention. Asshown, the method uses a combination of steps including a way ofpositioning a micro-mirror at a first activated position, rotating themicro-mirror, and positioning the micro-mirror at a second activatedposition according to an embodiment of the present invention. Otheralternatives can also be provided where steps are added, one or moresteps are removed, or one or more steps are provided in a differentsequence without departing from the scope of the claims herein.

Table 1 shows the angular rotation angle in degrees for a mirrorswitching operation as a function of the switching speed in microsecondsand the average angular rotation rate in degrees per microsecond forMEMS according to an embodiment of the present invention. Referring tothe first row of data, for rotation of a micro-mirror from −12° to +12°(a total of 24°) in a time period of 6 μs, the average angular rotationrate is 4°/μs. As the switching speed increases for a given angle ofrotation, the average angular rotation rate increases as well.

TABLE 1 Angular Rotation Switching Speed Average Angular (°) (μs)Rotation Rate (°/μs) +/−12 6 4 +/−12 4 6 +/−12 3 8 +/−12 2 12 +/−12 1 24+/−12 0.5 48 +/−12 0.3 80 +/−14 6 4.67 +/−14 4 7 +/−14 3 9.33 +/−14 2 14+/−14 1 28 +/−14 0.5 56 +/−14 0.3 93.33 +/−15 6 5 +/−15 4 7.5 +/−15 3 10+/−15 2 15 +/−15 1 30 +/−15 0.5 60 +/−15 0.3 100

Embodiments of the present invention utilize high stiffness hinges thatprovide for rapid rotation of the mirror as illustrated in Table 1.Thus, as described above, in some embodiments of the present invention,the transition time from one activated position to another activatedposition is from about 0.3 μs to about 6.0 μs. Moreover, the highstiffness hinges provided by embodiments of the present invention enablethe micro-mirror to achieve a maximum rotation rate in a predeterminedrange, for example from about 4°/μs to about 100°/μs.

For a torsion spring hinge, the restoring torque T_(S) is equal to thetorsional spring constant k_(tor) times the angle of rotation θ:T_(S)=k_(tor)θ. The restoring force at a selected portion of the mirrorplate is equal to the restoring torque T_(S) present in the torsionspring hinge divided by the distance d from the torsion spring hinge tothe selected position. Thus, as the distance from the torsion springhinge to the contact point increases, the restoring force present at thecontact point available to overcome stiction forces decreases. Asillustrated in FIG. 2, the distance d is measured from the torsionspring hinge 232 to the landing posts 222 along a line perpendicular tothe diagonal of the mirror plate. For a given distance d between thetorsion spring hinge and the contact position, an increase in restoringtorque will provide increased resistance to stiction problems.

For torsion spring hinges provided by embodiments of the presentinvention, the torsion spring constant, k_(tor), is approximated as

$\begin{matrix}{k_{tor} \propto {\frac{{Thickness}_{hinge} \cdot {Width}_{hinge}^{3}}{{Length}_{hinge}}.}} & (1)\end{matrix}$Thus, embodiments of the present invention utilize torsion spring hingeswith increased thickness and/or width or decreased length to increasethe torsional spring constant and the restoring force present at a givencontact location.

Another design consideration in selecting the hinge dimensions is thevertical sag or bending observed in the torsion spring hinge. Inembodiments of the present invention, it is preferable to minimize theamount of sagging observed in the hinge since vertical sag results inunpredictability in the deflection angle. Vertical sag in the flexiblemember also results in clearance problems between the mirror plate andthe electrodes. In embodiments of the present invention utilizing amultilevel electrode as illustrated in FIG. 2, an increase in mirrorplate sagging will result in designs with smaller top electrodes,reducing the electrostatic attraction forces between the electrodes andthe mirror plate. In some embodiment, repulsion forces are not present.

The bending stiffness of a hinge is related to the vertical hinge springfactor k_(ver), which is approximated by:

$\begin{matrix}{k_{ver} \propto \frac{{Thickness}_{hinge}^{3} \cdot {Width}_{hinge}}{{Length}_{hinge}^{3}}} & (2)\end{matrix}$Relating the vertical bending stiffness to the torsional spring constantprovides a measure of the amount of sag present in a hinge of apredetermined geometry. In particular, minimizing the ratio between thetorsional spring constant and the vertical bending stiffness willminimize the vertical sag by increasing the vertical stiffness inrelation to the torsional spring constant:

$\begin{matrix}{\frac{k_{tor}}{k_{ver}} \propto \left( \frac{{Width}_{hinge} \cdot {Length}_{hinge}}{{Thickness}_{hinge}} \right)^{2}} & (3)\end{matrix}$Thus, embodiments of the present invention provide a torsion springhinge that is preferably characterized by a narrow width, short length,and large thickness.

To increase system reliability, it is preferable to maintain stresspresent in the hinge at a level below the yield strength of the hingematerial. Generally, it is expected that a shorter hinge will result ingreater stress than a longer hinge since the torsion per unit length islarger for a shorter spring. However, the present inventors have foundthat when two hinges of different length and the same torsionalstiffness are compared, the shorter hinge is not necessarilycharacterized by a higher maximum stress. We believe that the reason forthis result, without limiting the present invention, is that a longerhinge will experience greater sag, increasing stress in the longer hingedue to bending of the hinge.

Merely by way of example, a finite element analysis of two hingegeometries was performed. In the analysis, the first hinge had a lengthof 7.1 μm and a width of 0.3 μm and the second hinge had a length of 4.6μm and a width of 0.25 μm. Both hinges had a thickness of 0.425 μm and astiffness of about 40 μN-μm. Based on the results of the finite elementanalysis, the maximum Von Mises stress in the hinges in both cases wasthe same, namely 1.50 GPa. The longer hinge is characterized by abouttwice the amount of sag as the shorter hinge since the longer hinge isweaker in the vertical direction (i.e., the width times the length islarger). Although the torsion angle per unit length for the longer hingeis less than that for the shorter hinge, we believe the additional sagin the longer hinge results in both hinges having the same maximumstress.

This conclusion is further supported by our observation that hinges withdifferent lengths but similar torsion strengths have a different snap-involtage. The snap-in voltage is defined as the voltage at which themirror plate switches to an activated position. In particular, theinventors have found the snap-in voltage for the longer hinge is lessthan the snap-in voltage for the shorter hinge. We believe that thelower snap-in voltage observed for the longer hinge is due to anincreased amount of sag in the longer hinge, which results in a smallereffective gap between the mirror plate and the electrodes. Along withthe reduced snap-in voltage, the longer hinge is characterized by areduced snap-in mirror angle and reduced clearance between the mirrorplate and portions of the electrode structure. Based on this analysis,embodiments of the present invention provide micro-mirrors with flexiblemembers that are thicker and shorter than comparable conventionaldesigns.

In some embodiments of the present invention, the thickness of the hingeis equal to the thickness of the mirror plate. As described more fullyin U.S. patent application Ser. No. 10/756,936, entitled ReflectiveSpatial Light Modulator, previously referenced, some embodiments of thepresent invention utilize a single continuous layer of silicon (e.g.,single crystal silicon) to form the mirror plate and coplanar torsionspring hinge. Such a design is illustrated by mirror plate 230 in FIG.2. Thus, embodiments of the present invention provide flexible membersor hinges with a well defined thickness determined by semiconductorgrowth and processing parameters.

Accordingly, given a hinge thickness equal to the mirror platethickness, embodiments of the present invention provide predeterminedhinge widths and lengths to obtain a predetermined restoring force atcontact locations. Increases in torsion spring hinge stiffness, however,are typically accompanied by increases in the electrostatic force neededto rotate the micro-mirror from an unactivated state to an activatedstate. Additionally, increases in torsion spring hinge stiffness mayresult in increased impact energy.

It is also understood that the examples and embodiments described hereinare for illustrative purposes only and that various modifications orchanges in light thereof will be suggested to persons skilled in the artand are to be included within the spirit and purview of this applicationand scope of the appended claims.

1. A method of activating a micro-mirror, the method comprising:applying a first electrode voltage to one or more electrodes associatedwith the micro-mirror, wherein the micro-mirror is positioned at a firstpositive deflection angle during a portion of the application of thefirst electrode voltage; maintaining the first electrode voltage for afirst predetermined time; applying a second electrode voltage to the oneor more electrodes, wherein the micro-mirror rotates to a first negativedeflection angle during a portion of the application of the secondelectrode voltage; maintaining the second electrode voltage for a secondpredetermined time; and applying a third electrode voltage to the one ormore electrodes and maintaining the third electrode voltage for a thirdpredetermined time, thereby: positioning the micro-mirror at a secondpositive deflection angle greater than the first positive deflectionangle during a first portion of the application of the third electrodevoltage; and subsequently positioning the micro-mirror at a thirdpositive deflection angle greater than the second positive deflectionangle during a second portion of the application of the third electrodevoltage, wherein the third positive deflection angle is a maximumdeflection angle for the micro-mirror.
 2. The method of claim 1 furthercomprising maintaining the micro-mirror at the third positive deflectionangle for a fourth predetermined time.
 3. The method of claim 1 whereinthe third electrode voltage is less than 90% of the static snap-involtage.
 4. The method of claim 1 wherein the first positive deflectionangle and the first negative deflection angle are measured with respectto an unactivated position.
 5. The method of claim 1 wherein the secondelectrode voltage is equal to a ground voltage.
 6. The method of claim 1wherein the first electrode voltage and the third electrode voltage areof unequal amplitudes.
 7. A method of operating a micro-mirror for aspatial light modulator, the method comprising: applying a firstelectrode voltage to an electrode of the micro-mirror; positioning themicro-mirror at a first position characterized by a negative maximumdeflection angle, wherein the micro-mirror is maintained at the firstposition through the application of a second electrode voltage;maintaining the micro-mirror at the first position for a predeterminednon-zero time; rotating the micro-mirror; and positioning themicro-mirror at a second position characterized by a positive maximumdeflection angle, wherein the micro-mirror is positioned at the secondposition through the application of a third electrode voltage less thana static snap-in voltage.
 8. The method of claim 7 wherein the thirdelectrode voltage is less than 90% of the static snap-in voltage.
 9. Themethod of claim 8 wherein the third electrode voltage is less than 80%of the static snap-in voltage.
 10. The method of claim 7 wherein thefirst and second electrode voltages are less than the static snap-involtage.
 11. The method of claim 7 wherein the first electrode voltageis greater than the second electrode voltage.
 12. The method of claim 11wherein the first electrode voltage is greater than or equal to thestatic snap-in voltage.
 13. The method of claim 7 wherein rotating themirror comprises reducing the second electrode voltage.
 14. The methodof claim 7 wherein the negative maximum deflection angle and thepositive maximum deflection angle are complementary.
 15. The method ofclaim 14 wherein the positive maximum deflection angle is about 12° andthe negative maximum deflection angle is about −12°.
 16. The method ofclaim 14 wherein the positive maximum deflection angle is greater than12° and the negative maximum deflection angle is greater than −12°. 17.A method of operating a micro-mirror for a spatial light modulator, themethod comprising: positioning the micro-mirror at a first positioncharacterized by a negative maximum deflection angle; rotating themicro-mirror to a second position characterized by a positive deflectionangle, wherein an absolute value of the positive deflection angle isgreater than zero and less than an absolute value of the negativemaximum deflection angle; then applying an electrode voltage to positionthe micro-mirror at a third position characterized by a positive maximumdeflection angle; and maintaining the micro-mirror at the positivemaximum deflection angle for a predetermined non-zero time.
 18. Themethod of claim 17 wherein the electrode voltage is applied upondetermining that the micro-mirror has rotated to the second position.19. The method of claim 17 wherein the electrode voltage is appliedbefore the micro-mirror begins counter-rotating toward the firstdeflection angle.
 20. The method of claim 17 wherein the electrodevoltage is at least 10% less than a static snap-in voltage.
 21. Themethod of claim 20 wherein the electrode voltage is at least 20% lessthan a static snap-in voltage.
 22. The method of claim 17 wherein anabsolute value of the positive maximum deflection angle is greater thanthe absolute value of the positive deflection angle.
 23. The method ofclaim 22 wherein the absolute value of the negative maximum deflectionangle and the absolute value of the positive maximum deflection angleare equal.
 24. The method of claim 17 wherein a predetermined delay timeis present between a time associated with rotating the micro-mirror to asecond position and a time associated with applying the electrodevoltage.
 25. The method of claim 24 wherein the predetermined delay timeis less than 2.0 μs.
 26. The method of claim 17 wherein the positivedeflection angle is a dynamic snap-in angle.
 27. A method of operating amicro-mirror of a spatial light modulator for display applications, themethod comprising: resonantly activating the micro-mirror, whereinresonantly activating the micro-mirror comprises: applying a firstelectrode voltage to one or more electrodes associated with themicro-mirror, wherein the micro-mirror is positioned at a first positivedeflection angle during a portion of the application of the firstelectrode voltage; maintaining the first electrode voltage for a firstpredetermined time; applying a second electrode voltage to the one ormore electrodes, wherein the micro-mirror rotates to a first negativedeflection angle during a portion of the application of the secondelectrode voltage; maintaining the second electrode voltage for a secondpredetermined time; and applying a third electrode voltage to the one ormore electrodes to snap-in the micro-mirror to a first activatedposition characterized by a first activated angle; dynamically switchingthe micro-mirror from the first activated position to a second activatedposition, wherein dynamically switching the micro-mirror comprises:removing the third electrode voltage, thereby freeing the micro-mirrorto rotate the micro-mirror to a dynamic angle position, wherein anabsolute value of the dynamic angle is greater than zero and less thanan absolute value of the first activated angle; and applying anelectrode voltage to position the micro-mirror at the second activatedposition.
 28. The method of claim 27 wherein the micro-mirror rotatesfrom the first activated position to the second activated position in atime period less than 6.0 μs.
 29. The method of claim 28 wherein themicro-mirror rotates from the first activated position to the secondactivated position in a time period less than 2 μs.
 30. The method ofclaim 27 wherein the first activated position is characterized by apositive deflection angle.
 31. The method of claim 27 wherein theelectrode voltage is less than a static snap-in voltage.
 32. The methodof claim 27 wherein the electrode voltage is at least 10% less than astatic snap-in voltage.
 33. The method of claim 32 wherein the electrodevoltage is at least 20% less than a static snap-in voltage.
 34. Themethod of claim 7 wherein the first electrode voltage and the secondelectrode voltage are of equal amplitudes.
 35. The method of claim 7further comprising maintaining the micro-mirror at the second positionfor a predetermined non-zero time.
 36. The method of claim 1 wherein thethird electrode voltage is less than a static snap-in voltage.